STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1-Basic theory and simple methods of adjustment

Abstract

Measurement error and misclassification of variables frequently occur in epidemiology and involve variables important to public health. Their presence can impact strongly on results of statistical analyses involving such variables. However, investigators commonly fail to pay attention to biases resulting from such mismeasurement. We provide, in two parts, an overview of the types of error that occur, their impacts on analytic results, and statistical methods to mitigate the biases that they cause. In this first part, we review different types of measurement error and misclassification, emphasizing the classical, linear, and Berkson models, and on the concepts of nondifferential and differential error. We describe the impacts of these types of error in covariates and in outcome variables on various analyses, including estimation and testing in regression models and estimating distributions. We outline types of ancillary studies required to provide information about such errors and discuss the implications of covariate measurement error for study design. Methods for ascertaining sample size requirements are outlined, both for ancillary studies designed to provide information about measurement error and for main studies where the exposure of interest is measured with error. We describe two of the simpler methods, regression calibration and simulation extrapolation (SIMEX), that adjust for bias in regression coefficients caused by measurement error in continuous covariates, and illustrate their use through examples drawn from the Observing Protein and Energy (OPEN) dietary validation study. Finally, we review software available for implementing these methods. The second part of the article deals with more advanced topics.

Keywords: Berkson error; SIMEX; classical error; differential error; measurement error; misclassification; nondifferential error; regression calibration; sample size; simulation extrapolation.

Figure 1:

Simulated data on 20 individuals showing the effects of classical error and Berkson error in the continuous covariate X on the fitted regression line. For both plots Y was generated from a normal distribution with mean β₀ + β_XX (using β₀ = 0, β_X = 1) and variance 1. Classical error plot: X was generated from a normal distribution with mean 0 and variance 1. X* was generated using X* = X + U. The difference in the slopes in this graph is due to attenuation from the measurement error in X. Berkson error plot:X* was generated from a normal distribution with mean 0 and variance 1 and X was generated from the normal distribution implied by the Berkson error model X = X* + U. For both error types var(U) = 3. The small difference in the slopes in this graph is due entirely to sampling error.

Figure 2:

Effects of non-differential misclassification in binary X on the regression coefficient in a linear regression of continuous Y on X. β_X is the regression coefficient in a regression of Y on X and ${\beta }_X^{*}$ is the regression coefficient in a regression of Y on X* (misclassified X). The attenuation factor λ (equation (13)) is a function of Pr(X = 1) and the sensitivity (Sn) and specificity (Sp) of X*. The thick line is the line ${\beta }_X^{*}={\beta }_X$.

Figure 3:

Simulated data on 20 individuals showing the effects of classical error and Berkson error in continuous Y on the fitted regression line. For both plots X was generated from a normal distribution with mean 0, variance 1 and the errors U were generated from a normal distribution with mean 0 and variance 3. Classical error plot: Y was generated with mean X and variance 1. Y* was generated using Y* = Y + U. The difference in slopes is due entirely to sampling error. Berkson error plot: Y* was generated with mean X and variance 1. The difference in slopes is due to attenuation from the measurement error in Y. Y given X was generated from the normal distribution implied by the model for Y* and the Berkson error model Y = Y* + U.

Figure 4:

Effects of non-differential and differential misclassification in Y on the log odds ratio. ${\beta }_X^{*}$ is the log odds ratio of Y* given X (equation (20)) and β_X is the log odds ratio for Y given X (equation (19)). The covariate X is binary (for simplicity) and we assume β₀ = 0 in equation (19). Sn and Sp denote the non-differential sensitivity and specificity for Y*, and Sn(X) and Sp(X) denote the differential versions for X = 0,1. The thick line is the line ${\beta }_X^{*}={\beta }_X$.

Figure 5:

SIMEX: Relationship between the measurement error variance var(U) and the regression coefficient ${\mathrm{\beta }}_{\mathrm{X}}^{\mathrm{*}}$. β_X is the regression coefficient in a regression of Y on X and ${\beta }_X^{*}$ is the regression coefficient in a regression of Y on X*. X* is assumed to follow the classical error model X* = X + U, and ${\mathrm{\beta }}_{\mathrm{X}}^{\mathrm{*}}=\frac{\mathrm{v}\mathrm{a}\mathrm{r}(\mathrm{X})}{\mathrm{v}\mathrm{a}\mathrm{r}(\mathrm{X})+\mathrm{v}\mathrm{a}\mathrm{r}(\mathrm{U})}{\mathrm{\beta }}_{\mathrm{X}}$. Here, var(X) = 1 and β_X = 1.

Figure 6:

SIMEX estimation for the association between individual heart rate as outcome variable and log-transformed individual particle number concentration (a measure of air pollution exposure) measured in number per cm³. The SIMEX estimator is assessed assuming a measurement error variance of 0.03, which is determined through comparison measurements, a quadratic extrapolation function, number of simulations B = 100 and s = (1,1.5,2,2.5,3). The analysis is based on longitudinal data of an observational study described in Peters et al (2015). The model accounts for temperature, relative humidity, time trend and time of the day. The solid curve is obtained from the fit of the extrapolation model to the pseudo-datasets, and the dotted line represents the extrapolated part.